geometry

Table of Contents

Introduction
Major branches of geometry
- Euclidean geometry
- Analytic geometry
- Projective geometry
- Differential geometry
- Non-Euclidean geometries
- Topology
History of geometry
- Ancient geometry: practical and empirical
  - Finding the right angle
  - Locating the inaccessible
  - Estimating the wealth
- Ancient geometry: abstract and applied
  - The three classical problems
    - Doubling the cube
    - Trisecting the angle
    - Squaring the circle
  - Idealization and proof
  - The Euclidean synthesis
  - Gnomonics and the cone
  - Astronomy and trigonometry
    - Calculation
    - Epistemology
- Ancient geometry: cosmological and metaphysical
  - Pythagorean numbers and Platonic solids
  - Measuring the Earth and heavens
- The post-classical period
  - Passage through Islam
  - Europe rediscovers the classics
  - Linear perspective
- Transformation
  - French circles
    - Projective geometry
    - Cartesian geometry
  - Geometrical calculus
  - The world system
- Relaxation and rigour
  - Projection again
  - Non-Euclidean geometries
  - A grand synthesis
  - The real world

References & Edit History Related Topics

Images & Videos

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geometry

mathematics

Written by J.L. Heilbron

Fact-checked by The Editors of Encyclopaedia Britannica

Last Updated: Nov 19, 2024 • Article History

Key People:: Blaise Pascal; Euclid; Ptolemy; Pierre de Fermat; Bernhard Riemann

Related Topics:: topology; Euclidean geometry; analytic geometry; differential geometry; projective geometry

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geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space. It is one of the oldest branches of mathematics, having arisen in response to such practical problems as those found in surveying, and its name is derived from Greek words meaning “Earth measurement.” Eventually it was realized that geometry need not be limited to the study of flat surfaces (plane geometry) and rigid three-dimensional objects (solid geometry) but that even the most abstract thoughts and images might be represented and developed in geometric terms. This article begins ...(100 of 9409 words)

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